Area of triangle PST in terms of triangle PQR

Question

In the triangle PQR $QT=TR$, $PS=1 cm$ , $SQ=2 cm$ , How should I be writing the area of $\triangle PST$ in terms of $\triangle PQR $

Answer 1

Since $|\overline{QT}|=|\overline{TR}|$ it follows that $\triangle PQT$ and $\triangle PTR$ have equal areas, so $$[PQT]=\frac12[PQR]$$ where $[\mathcal{P}]$ means area of $\mathcal{P}$. From $|\overline{PS}|=\frac12|\overline{SQ}|$ it follows that the area of $\triangle PST$ is a half of the area of $\triangle PQT$, then $$[PST]=\frac13[PQT]=\frac16[PQR]$$